Quantum generative models for sampling many-body spectral functions

Abstract

Quantum generative models for sampling many-body spectral functions are provided. Quantum approximate Bayesian computation is provided for NMR model inference.

What is claimed is: 
     
         1 . A method comprising:
 preparing a state on a quantum computer, the state corresponding to a physical property;   evolving the state on the quantum computer, said evolution corresponding to a Hamiltonian having a plurality of parameters, the plurality of parameters corresponding to a hypothetical molecule;   sampling the state after said evolution, thereby determining hypothetical observations of the hypothetical molecule.   
     
     
         2 . The method of  claim 1 , further comprising:
 comparing the hypothetical observations to actual observations;   based on said comparing, varying the plurality of parameters to minimize a difference between the hypothetical observations and the actual observations.   
     
     
         3 . The method of  claim 2 , wherein said varying the plurality of parameters comprises variational Bayesian inference or gradient descent. 
     
     
         4 . The method of  claim 1 , wherein the hypothetical observations comprise spectra. 
     
     
         5 . The method of  claim 1 , wherein the quantum computer comprises a plurality of system qubits, and wherein said sampling further comprises:
 measuring the plurality of system qubits.   
     
     
         6 . The method of  claim 5 , wherein said sampling further comprises:
 applying a fast Fourier transform to determine a spectrum corresponding to the hypothetical molecule.   
     
     
         7 . The method of  claim 1 , wherein the quantum computer comprises a plurality of system qubits and a plurality of control qubits, each of the plurality of control qubits corresponding to one of the plurality of system qubits, the method further comprising:
 initializing the plurality of control qubits according to an equal superposition of all controls.   
     
     
         8 . The method of  claim 7 , wherein said sampling further comprises:
 measuring the plurality of control qubits.   
     
     
         9 . The method of  claim 7 , wherein said sampling further comprises:
 applying a quantum fast Fourier transform to determine a spectrum corresponding to the hypothetical molecule.   
     
     
         10 . The method of  claim 7 , wherein said preparing further comprises:
 preparing the plurality of system qubits with an initial state;   coupling each of the plurality of system qubits with one of the plurality of control qubits;   coupling an ancilla qubit to an operator, the operator corresponding to the physical property;   coupling each system qubit and its corresponding control qubit to the ancilla qubit;   measuring the ancilla qubit.   
     
     
         11 . The method of  claim 10 , wherein coupling each system qubit and its corresponding control qubit to the ancilla qubit comprises applying a Hadamard gate to each system qubit. 
     
     
         12 . The method of  claim 1 , wherein sampling comprises uniform sampling or importance sampling. 
     
     
         13 . A system comprising:
 a quantum computer; and   a computing node, wherein
 the computing node is configured to prepare a state on the quantum computer, 
 the state corresponding to a physical property, 
 the quantum computer is configured to evolve the state, said evolution corresponding to a Hamiltonian having a plurality of parameters, the plurality of parameters corresponding to a hypothetical molecule, and 
 the computing node is configured to sample the state after said evolution, thereby determining hypothetical observations of the hypothetical molecule. 
   
     
     
         14 . The system of  claim 13 , wherein the computing node is configured to:
 compare the hypothetical observations to actual observations;   based on said comparing, varying the plurality of parameters to minimize a difference between the hypothetical observations and the actual observations.   
     
     
         15 . The system of  claim 13 , wherein the quantum computer comprises a plurality of system qubits, and wherein said sampling further comprises:
 measuring the plurality of system qubits.   
     
     
         16 . The system of  claim 13 , wherein the quantum computer comprises a plurality of system qubits and a plurality of control qubits, each of the plurality of control qubits corresponding to one of the plurality of system qubits, wherein the computing node is configured to:
 initialize the plurality of control qubits according to an equal superposition of all controls.   
     
     
         17 . The system of  claim 16 , wherein said sampling further comprises:
 applying a quantum fast Fourier transform to determine a spectrum corresponding to the hypothetical molecule.   
     
     
         18 . The system of  claim 16 , wherein:
 the computing node is configured to prepare the plurality of system qubits with an initial state;   the quantum computer is configured to couple each of the plurality of system qubits with one of the plurality of control qubits;   the quantum computer is configured to couple an ancilla qubit to an operator, the operator corresponding to the physical property;   the quantum computer is configured to couple each system qubit and its corresponding control qubit to the ancilla qubit; and   the computing node is configured to measure the ancilla qubit.   
     
     
         19 . The system of claim  21 , wherein coupling each system qubit and its corresponding control qubit to the ancilla qubit comprises applying a Hadamard gate to each system qubit. 
     
     
         20 . A computer program product for sampling many-body spectral functions, the computer program product comprising a computer readable storage medium having program instructions embodied therewith, the program instructions executable to perform a method comprising:
 preparing a state on a quantum computer, the state corresponding to a physical property;   evolving the state on the quantum computer, said evolution corresponding to a Hamiltonian having a plurality of parameters, the plurality of parameters corresponding to a hypothetical molecule;   sampling the state after said evolution, thereby determining hypothetical observations of the hypothetical molecule.